Expection of Angular Momentum

Homework Statement

I am trying to calculate the expectation of the y-component of the angular momentum L.
$<L_{y}>$. How should I approach this?

Homework Equations

I try to write it in terms of the following commutator

$L(y) = \frac{2*pi}{ih} [L_{x}, L_{z}]$

The Attempt at a Solution

Avodyne
What do you know about the state in which you are to take the expectation value?

What do you know about the state in which you are to take the expectation value?

Hi there, the state is given as |l, m>, where l is the orbital angular momentum quantum number, and m is the magnetic moment quantum number.

I want to prove that to compute <l,m| L(y) |l,m> = <L(y)> =0, how should I approach this?

Many thanks!

gabbagabbahey
Homework Helper
Gold Member
If I were you, I'd write $L_y$ in terms of the raising and lowering operators $L_{\pm}$...

If I were you, I'd write $L_y$ in terms of the raising and lowering operators $L_{\pm}$...

I was told that I have to use the commutation relation between the L(x) and L^2 to get the expectation value of L(y). How can I do that though?

Thanks

gabbagabbahey
Homework Helper
Gold Member